X-ray interferometric imaging system

ABSTRACT

An x-ray interferometric imaging system includes an x-ray source with a target having a plurality of discrete structures arranged in a periodic pattern. The system further includes a beam-splitting x-ray grating, a stage configured to hold an object to be imaged, and an x-ray detector having a two-dimensional array of x-ray detecting elements. The object is positioned between the beam-splitting x-ray grating and the x-ray detector, the x-ray detector is positioned to detect the x-rays diffracted by the beam-splitting x-ray grating and perturbed by the object to be imaged.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a Continuation of U.S. patent applicationSer. No. 14/527,523, entitled “X-ray Interferometric Imaging System” andfiled Oct. 29, 2014, and which in turn claims the benefit of U.S.Provisional Patent Application Nos. 61/898,019, entitled “X-ray PhaseContrast imaging System” and filed on Oct. 31, 2013; 61/901,361,entitled “An X-ray Source Consisting of an Array of Fine Sub-Sources”and filed on Nov. 7, 2013; and 61/981,098 entitled “Two DimensionalPhase Contrast Imaging Apparatus” and filed Apr. 17, 2014, all of whichare incorporated herein by reference in their entirety.

FIELD OF THE INVENTION

The embodiments of the invention disclosed herein relate tointerferometric imaging systems using x-rays, and in particular,interferometric imaging systems comprising high-brightness sources ofx-rays for generating phase-contrast images. The high brightness x-raysources may use anodes or targets comprising periodic microstructures ofx-ray generating materials embedded in a thermally conducting substrateof low atomic number material.

BACKGROUND OF THE INVENTION

The initial discovery of x-rays by Röntgen in 1895 [W. C. Röntgen, “EineNeue Art von Strahlen (Würzburg Verlag, 1896); “On a New Kind of Rays,”Nature, Vol. 53, pp. 274-276 (Jan. 23 1896)] occurred when Röntgen wasexperimenting with electron bombardment of targets in vacuum tubes. Thecontrast between the absorption from bone containing calcium (atomicnumber Z=20) and soft tissue containing mostly carbon (Z=6), wasimmediately apparent because the absorption difference between the twomaterials at x-ray energies between 5 and 30 keV can differ by a factorof 10 or more, as illustrated in FIG. 1. These high energy, shortwavelength photons are now routinely used for medical applications anddiagnostic evaluations, as well as for security screening, industrialinspection, quality control and failure analysis, and for scientificapplications such as crystallography, tomography, x-ray fluorescenceanalysis and the like.

Although x-ray shadowgraphs have become a standard medical diagnostictool, there are problems with simple absorption contrast imaging.Notably, for tests such as mammograms, variations in biological tissuemay result in only a subtle x-ray absorption image contrast, makingunambiguous detection of tumors or anomalous tissue difficult.

In the past decade, a new kind of x-ray imaging methodology has emerged,based on x-ray phase contrast interferometry. The method relies on thewell-known Talbot interference effect, originally observed in 1837 [H.F. Talbot, “Facts relating to optical science No. IV”, Philos. Mag. vol.9, pp. 401-407, 1836] and fully explained by Lord Rayleigh in 1881 [LordRayleigh, “On copying diffraction gratings and some phenomena connectedtherewith,” Philos. Mag. vol. 11, pp. 196-205 (1881)].

This effect is illustrated in FIG. 2. For an absorbing grating G ofperiod p, the diffraction pattern from a monochromatic beam of awavelength λ with sufficient coherence forms a repeating interferencepattern that reconstructs the original grating pattern, (known as a“self-image”) at multiples of a distance known as the Talbot DistanceD_(T). For the case when the incident beam is a plane wave (equivalentto a source located at infinity from the grating G), D_(T) is given by:

$\begin{matrix}{D_{T} = \frac{2\; p^{2}}{\lambda}} & \left\lbrack {{Eqn}.\mspace{14mu} 1} \right\rbrack\end{matrix}$

Between the grating G and the Talbot Distance, other periodicinterference patterns emerge as well. The periodicity and the positionof the Talbot fringes depend on the transmission properties of thegrating G, including amount of phase-shift and percent of absorption,and grating line-to-space (opening) ratio, or duty factor. For example,for a periodic absorption grating, a fringe pattern that reconstructs ofthe original grating pattern with a lateral shift by half the gratingperiod occurs at half the Talbot Distance D_(T)/2, and a fringe patternwith a period of half of the original grating period occurs at onequarter of the Talbot Distance D_(T)/4 and at three quarters of theTalbot Distance 3D_(T)/4, as illustrated in FIG. 2. These 2-Dinterference patterns are sometimes called a “Talbot Carpet” because ofthe resemblance of these complex patterns to ornate oriental carpets.[Note: this image of an Optical Talbot Carpet in FIG. 2 is adapted froma file created by Ben Goodman and available at<http://commons.wikimedia.org/wiki/File:Optical_Talbot_Carpet.png>.]

FIGS. 3 and 4 illustrate a prior art Talbot interferometric comprising apartially coherent source 200 (shown as a microfocus source) of x-rays288 and a beam splitting grating G₁ 210 of period p₁ that establishes aset of Talbot interference fringe patterns 289. It should be noted thatthe coherence length of the x-ray source is preferably set to becomparable to or larger than the period p₁ of the beam splitting gratingG₁ 210, so that the Talbot interference fringes will have high contrast.The beam splitting grating 210 may be an amplitude (also known anabsorption or transmission) grating, creating intensity fringes asillustrated in FIG. 2, but is more typically a phase grating forefficient use of the illuminating x-rays, introducing periodicphase-shifts to the x-ray pattern that also form periodic Talbot fringes289. Henceforth in this application, a transmission grating will be usedto describe gratings in which the x-ray transmission through the gratinglines is less than 10% and a phase grating will be used to describegratings in which the phase shift through the grating lines is afraction (e.g. ½) or odd integer multiple of π.

The Talbot fringes 289 are detected using an x-ray detector 290,preferably with a spatial resolution equal to or better than one thirdof the Talbot fringe period and having a high x-ray quantum detectionefficiency. The detector 290 transforms the x-ray intensity pattern intoelectronic signals that are transmitted over a connector 291 to an imageprocessing system 295. When an object is placed in the beam path, theimage processing system 295 is used to process the x-ray intensitypattern intensity information 298 to obtain absorption, phase, andscattering contrast images.

In practice, the spatial resolution of the detector 290 (such as a flatpanel detector, or a charge coupled device (CCD) detector coupled with ascintillator that converts x-rays to visible light) is often on theorder of tens of micrometers or larger, and the Talbot fringes 289 maybe too fine to detect directly with the detector 290. In this case, ananalyzer grating G₂ 220 of period p₂ is often used to produce Moiréfringes. To record a complete set of images, the analyzer grating G₂ 220will be moved in predetermined distances orthogonal to the gratingperiod and relative to the detector to collect multiple interferencepatterns in a process called “phase-stepping”, or less commonly, rotatedat a small angle relative to G₁ to obtain a Moiré pattern in asingle-shot image for Fourier analysis. The image(s) are then processedto reconstruct the wavefront and determine the shapes, structures, andcomposition of the objects that created them.

It should also be noted that, instead of physically moving the analyzergrating 220, the position of the x-ray source may also be displaced tocreate a translation of the interference images that allows thecollection of phase-shift information. This can be accomplishedelectronically by moving the position of the electron beam that bombardsthe x-ray generating material that serves as the source for the x-rays[see, for example, H. Miao et al., “Motionless phase stepping in X-rayphase contrast imaging with a compact source”, Proceedings of theNational Academy of Sciences, vol. 110(48) pp. 19268-19272, 2013] or byphysically moving the x-ray source relative to a fixed position of theanalyzer grating 220.

These grating-based x-ray phase-contrast imaging (XPCI) techniques aregenerally referred to as “grating-based interferometry” (GBI).

As illustrated so far, the grating interferometer only producesinterference fringes, and the analysis of these fringes will reveal thestructure of the already known grating G₁ 210 or the wavefront of theillumination beam. However, when an object is introduced in the path ofthe x-ray beam, variations in the wavefront introduced by the objectresult in corresponding changes in the pattern of the Talbotinterference fringes, generally known as Moiré fringes. Interferometricimage reconstruction techniques may then be used to analyze thewavefront and reconstruct images representing the structure of theunknown object.

In FIG. 5, the prior art Talbot interferometer of FIGS. 3 and 4 isillustrated being used as an imaging technique for a biological sample,in this case, a mouse 240-M, placed between the source 200 and the beamsplitting grating G₁ 210. The x-rays 288 from the coherent source 200pass through the mouse 240-M and the beam splitting grating G₁ 210 andcreate a perturbed set of Talbot fringes 289-M. The local phase shiftscreate angular deviations that translate into changes of locallytransmitted intensity when analyzed by the analyzer grating G₂ 220 anddetector 290. Collecting multiple images from the x-ray detector 290 forsituations where the analyzer grating G₂ 220 has been displaced bymultiple predetermined positions allow a recording of the interferencepattern 289-M.

As before, the detector 290 transforms the x-ray intensity pattern intoelectronic signals that transmitted over a connector 291 to an imageprocessing system 295 used to produce one or more images 298-M withabsorption, differential phase, phase, and scattering contrastinformation. Numerical processing of the images, including imagescollected by the system with and without the object under investigation,can be used to infer the shapes and structure of the objects thatcreated them, including objects such as the mouse 240-M. The recordedintensity oscillations can be represented by a Fourier series, and withthe proper image processing algorithms, differential phase shift andabsorption signals can be extracted, and images corresponding to x-rayabsorption, phase contrast, and scattering by the object can besynthesized. [See, for example, A. Momose et al., “Demonstration ofx-ray Talbot interferometry”, Jpn. J. Appl. Phys. 42, pp. L866-L868,2003; A. Momose, U.S. Pat. No. 7,180,979, issued Feb. 20, 2007; and T.Weitkamp et al. “Hard X-ray phase imaging and tomography with a gratinginterferometer”, Proc. SPIE vol 5535, pp. 137-142, 2004, and “X-rayphase imaging with a grating interferometer”, Optics Express vol.13(16), pp. 6296-6304, 2005.]

It should be noted that other configurations exist in which the object,such as a mouse 240-M, can be placed between the beam splitting gratingG₁ 210-A and the analyzer grating G₂ 220 and detector 290, asillustrated in FIG. 6. Other configurations using various phase andamplitude gratings, or using detector 290 with higher resolution pixelswithout the analyzer grating 220, may also be known to those skilled inthe art.

Aside from imaging the anatomy of mice, clinical applications ofphase-contrast x-ray imaging may be found in mammography, where thedensity of cancerous tissue may have a distinct phase signature fromhealthy tissue [see, for example, J. Keyriläinen et al., “Phase contrastX-ray imaging of breast”, Acta Radiologica vol. 51 (8) pp. 866-884,2010], or for bone diseases like osteoporosis or osteoarthritis, inwhich the angular orientation of the bone structures may be an earlyindicator of bone disease [See, for example, P. Coan et al., “In vivox-ray phase contrast analyzer-based imaging for longitudinalosteoarthritis studies in guinea pigs”, Phys. Med. Biol. vol. 55(24),pp. 7649-62, 2010].

However, for the prior art configurations described so far, x-ray poweris a problem. An x-ray source with a full-width half maximum diameter Sgiven by

$\begin{matrix}{S \leq \frac{\lambda\; L}{2\pi\; p_{1}}} & \left\lbrack {{Eqn}.\mspace{14mu} 2} \right\rbrack\end{matrix}$where p₁ is the period of the beam splitting grating G₁ 210 and L thedistance between the source 200 and the beam splitting grating G₁ 210,is required for the technique to produce high contrast fringes and Moirépatterns. For practical applications and system geometries, this impliesa microfocus source. However, electron bombardment of the target alsocauses heating, and the x-ray power that can be achieved is limited bythe maximum total electron power that can fall on the microspot withoutmelting the x-ray generating material. A limited electron power means alimited x-ray power, and the low x-ray flux achievable with typicalx-ray targets may lead to unacceptable long exposure times when used,for example, for mammography or other diagnostic tests involving livepatients or animals. The total x-ray flux can be increased bydistributing higher electron power over a larger area, but then thesource becomes less coherent, degrading the image contrast.

Coherent x-rays of higher brightness and sufficient flux can be achievedby using a synchrotron or free-electron laser x-ray source, but thesemachines may occupy facilities that cover acres of land, and areimpractical for use in clinical environments.

One innovation that has been shown to enable greater x-ray power employsan additional grating G₀ [see, for example, John F. Clauser, U.S. Pat.No. 5,812,629, issued Sep. 22, 1998]. Such a system is illustrated inFIG. 7. In this configuration, a source grating G₀ 308 with period p₀,which is typically an x-ray transmission grating, is used in front of anx-ray source 300. In this case, the x-ray source may be a high-powerextended source with a large incident electron beam area (and not amicrofocus source) that produces a higher total flux of x-rays.

The x-rays 388 pass through the grating G₀ 308 and emerge from thegrating apertures as an array of individually spatially coherent(similar to a microfocus source described above) but mutually incoherentsub-sources of illumination for the beam splitting grating G₁. To ensurethat each x-ray sub-source in G₀ contributes constructively to theimage-formation process, the geometry of the setup should satisfy thecondition:

$\begin{matrix}{p_{0} = {p_{2}\frac{L}{D}}} & \left\lbrack {{Eqn}.\mspace{14mu} 3} \right\rbrack\end{matrix}$When the condition is met, the x-rays from the many apertures of G₀produce the same (overlapping) Talbot interference pattern, and becausethe various mutually incoherent sources do not interfere with eachother, these Talbot patterns will add as intensities. The effect at thedetector 290 is therefore to simply increasing the signal (along with itthe signal-to-noise ratio) over what a single coherent source canprovide.

This configuration is called the Talbot-Lau interferometer [see FranzPfeiffer et al., “Phase retrieval and differential phase-contrastimaging with low-brilliance X-ray sources”, Nature Physics vol. 2, pp.258-261, 2006; and also Described in U.S. Pat. No. 7,889,838 byChristian David, Franz Pfeiffer and Timm Weitkamp, issued Feb. 15,2011].

FIG. 8 illustrates x-ray images of a live mouse collected using aTalbot-Lau interferometer, as reported by Martin Bech [M. Bech et al.,“In-vivo dark-field and phase-contrast x-ray imaging”, ScientificReports 3, Article number: 3209, 2013, FIG. 1]. The x-ray energy usedwas 31 keV, and the gratings were fabricated by lithographically etchingstructures in silicon (Z=14). Absorption gratings G₀ for the source andG₂ for the analyzer were created by additionally coating the patternedsilicon with gold (Z=79).

All of the images of FIG. 8 were reported as reconstructed from the sameset of 5 interferometric images, each collected over an exposure time of10 seconds. The raw images were Fourier processed and ramp corrected toobtain the three image modalities. FIG. 8A illustrates an intensityimage based on x-ray attenuation, showing the absorption contrastbetween the bones and soft tissue. FIG. 8B illustrates a phase-contrastimage, which clearly identifies soft tissue structures such as thetrachea (illustrated with an arrow). FIG. 8C illustrates an additionaldark-field contrast image due to x-ray scattering from fine featureswith linear dimensions less than the spatial resolution of the imagingsystem, which strongly highlights the fur and lungs.

Unfortunately, the current art of Talbot-Lau GBIs have many constraintsfor most practical applications such as clinical imaging, including arequirement that both the source grating G₀ and the analyzer grating G₂have fine pitches and apertures with large aspect ratios.

The requirement for the source grating G₀ is to create fine individualwell-separated x-ray sub-sources to minimize the reduction in imagecontrast due to unwanted transmission of x-rays through the aperturedefining structures. However, for a 1:1 line-to-space ratio grating,simple x-ray shadowing dictates that the x-ray transmission through thegrating is limited to less than 50%, and is reduced further when theangular shadowing (limiting the angular range of the x-rays from thesource to reach the object) is included. Furthermore, the optimalline-to-space ratio for G₀ that reduces the radiation dose to the object(which is important to preclinical and clinical imaging applications) iscloser to 3:1 rather than 1:1. In this case, about 75% of the x-raysfrom the source are blocked due to area shadowing alone, and whengratings with large aspect ratios are used, greater losses occur due toangular shadowing.

The requirement for the analyzer grating G₂ is to be able to sample theTalbot interference fringes with sufficient resolution without losingcontrast. As a result, both the G₀ and G₂ gratings must have smallapertures and be of thickness sufficient to minimize unwanted x-raytransmission, which limits the efficient use of the x-rays from thesource. Furthermore, the loss from the analyzer grating G₂ furtherresults in a significantly higher dose (relative to the same systemwithout a G₂ grating) for the object under investigation to produce animage with good characteristics due to multiple exposures forphase-stepping and absorption of x-rays resulting in lowersignal-to-noise. When the object under investigation is a live animal orhuman, higher doses of ionizing radiation are undesirable and generallydiscouraged.

If the aperture dimensions of the grating G₀ are larger, angularcollimation can be reduced (although not the area shadowing) so thatx-ray transmission is not reduced as severely, but this reduces thespatial coherence length of the x-ray beam downstream from theapertures, and leads a reduction in image contrast. Smaller aperturescan increase the possible image contrast and resolution by improvingspatial coherence, but decreases the overall number of x-rays in thesystem, thus requiring longer exposure times. Moreover, with smallerapertures, these fine gratings become more difficult to manufacture.

The problem is exacerbated when attempting to use a Talbot-Lauinterferometer for higher energy x-rays, which are often desired toobtain sufficient transmission through an object and to reduce rationdoes. In general, as was illustrated in FIG. 1, the absorption of x-raysfor biological tissue is far lower for x-rays with energy greater than 5keV, and the use of higher energy x-rays will reduce the absorbed doseof potentially harmful ionizing radiation by orders of magnitude.However, 5 keV photons have a wavelength of 0.248 nm, and 50 keV have awavelength 10 times smaller (0.0248 nm). Furthermore, building absorbinggratings such as G₀ and G₂ for these higher energy, shorter wavelengthx-rays can present difficulties, as the thickness of the gratings mustincrease exponentially to maintain the same absorption factor for higherenergy x-rays (the x-ray attenuation length is approximatelyproportional to E_(kev) ³).

The preceding problems of Talbot-Lau GBIs using linear gratings, whichcan be used for collecting interference data in one dimension only,become more severe if one wishes to generate phase-contrast images intwo orthogonal directions. This is often required to make the imagereconstruction robust and images more understandable, and becausefeatures parallel to the grating lines in the 1-D case are typicallyless accurately measured. One simple approach is to perform XPCI in twoorthogonal directions and then subsequently register the two datasetsproperly. In addition to challenges associated with the imaging andregistration processes, this approach may not be practical, especiallywhen used with living subjects who may move or simply become impatient,and who will incur increased dosage (doubled) if the phase stepping mustbe performed in two directions. Simultaneous two-dimensional XPCI wouldbe desirable, especially if data collection in a single exposure (shot)and at high x-ray energies is possible to reduce exposure times and theabsorbed dosage.

There is therefore a need for an x-ray interferometric imaging systemthat offers the resolution and detection capabilities of the Talbot-Lauinterferometer, but employing a brighter compact source of x-rays and,ideally, a brighter source of higher energy x-rays, especially one thatcould provide simultaneous two-dimensional phase-contrast imaging.

BRIEF SUMMARY OF THE INVENTION

We disclose here an x-ray interferometric imaging system in which thex-ray source comprises a target having a plurality of microstructuredx-ray generating materials arranged within a periodic array pattern toform periodic sub-sources of x-rays. The system additionally comprises abeam-splitting grating G₁ that creates a Talbot interference pattern,and an x-ray detector to convert two-dimensional x-ray intensities intoelectronic signals.

If the spatial resolution of the detector is equal to or better than onethird of the Talbot fringe period, the detector may record the fringesdirectly. The system may also comprise a second analyzer grating G₂ thatmay be placed in front of the detector to form additional interferencefringes, and a means to translate the analyzer grating G₂ relative tothe detector to create Moiré fringes at the detector. Additionally, thesystem may comprise a means of translating the phase grating G₁ relativeto the analyzer grating G₂.

The x-ray source target comprises a plurality of microstructures ofx-ray generating materials (such as molybdenum or tungsten) in closethermal contact with a thermally conducting substrate of a low atomicnumber material, such as diamond or beryllium. The x-ray generatingmicrostructures may be arranged in a periodic pattern, with eachperiodic element of the pattern corresponding to a single discretemicrostructure or alternatively, with each periodic element of thepattern comprising multiple discrete microstructures. One or moresources of electrons bombard the plurality of x-ray generatingmaterials, which are generally arranged within a periodic array, so thatthe x-ray generated from each periodic array element serves as anindividually coherent sub-source of x-rays of illumination for the beamsplitting grating G₁. In some embodiments, the microstructures havelateral dimensions measured on the order of microns, and with athickness on the order of one half of the electron penetration depthwithin the substrate material. In some embodiments, the microstructuresare formed in a regular two-dimensional array.

The beam splitting grating G₁ may be a phase grating or an absorptiongrating. The analyzer grating G₂ is generally a transmission grating.Both gratings G₁ and G₂ may be fabricated as lithographically producedmicrostructures in silicon, and may comprise 1-D structures, 2-Dstructures, or combinations thereof.

A particular advantage of the invention is that high x-ray brightnessand large x-ray power may be achieved by using an x-ray target in whichthe microstructures of a high Z material are in close thermal contactwith, or embedded in, a substrate of low Z material and high thermalconductivity, such as beryllium or diamond. The ability of the substrateto draw heat away from the x-ray generating material allows higherelectron density and power to be used, generating greater x-raybrightness and power from each of the sub-sources. This results in thecreation of individual, well-separated spatially coherent x-raysub-sources from the high Z material, while the use of a substrate withlow Z and low mass density minimizes the production of x-rays from thesubstrate that can lead to a reduction in image contrast.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a plot of the x-ray absorption of carbon and calciumas a function of x-ray energy.

FIG. 2 illustrates a prior art Talbot interference pattern produced by atransmission grating.

FIG. 3 illustrates a prior art x-ray grating interference system using amicrofocus source.

FIG. 4 illustrates a cross section view of the prior art x-ray gratinginterference system of FIG. 3.

FIG. 5 illustrates the prior art x-ray grating interference system ofFIG. 3 used to form an x-ray contrast image of a mouse.

FIG. 6 illustrates a variation of the prior art x-ray gratinginterference system of FIG. 3 used to form an x-ray contrast image of amouse.

FIG. 7 illustrates a prior art Talbot-Lau interferometer being used toform an x-ray contrast image of a mouse.

FIG. 8A illustrates a published x-ray absorption image of a mousegathered using a prior art Talbot-Lau interference system.

FIG. 8B illustrates a published x-ray phase-contrast image of a mousegathered using a prior art Talbot-Lau interference system.

FIG. 8C illustrates a published x-ray dark field scattering image of amouse gathered using a prior art Talbot-Lau interference system.

FIG. 9 illustrates a schematic cross-section view of an embodiment of anx-ray interferometric imaging system according to the invention.

FIG. 10 illustrates a schematic cross-section view of an embodiment ofthe invention.

FIG. 11 illustrates a perspective view of the embodiment of theinvention shown in FIG. 10, in which the x-ray target comprises twodimensional periodic array of x-ray generating microstructures.

FIG. 12 illustrates a detailed schematic cross-section view of theembodiment of the invention shown in FIGS. 10 and 11.

FIG. 13 illustrates a perspective view of an embodiment of the inventionin which the x-ray target comprises of x-ray generating microstructuresin the form of parallel lines.

FIG. 14 illustrates a perspective view of an embodiment of the inventionin which the object (a mouse) is placed between the gratings G₁ and G₂.

FIG. 15 illustrates a detailed schematic cross-section view of anembodiment of the invention in which a high-resolution detector is usedwithout an analyzer grating.

FIG. 16 illustrates a perspective view of an embodiment of the inventionin which the object (a mouse) is placed between the grating G₁ and thedetector, and the grating G₁ comprises a two-dimensional phasestructure.

FIG. 17 illustrates a perspective view of an embodiment of the inventionin which the object (a mouse) is placed between the source and thegrating G₁, and the grating G₁ comprises a two-dimensional phasestructure.

FIG. 18 illustrates a schematic cross-section view of an embodiment ofthe invention in which the target is mounted within the vacuum chamber.

FIG. 19 illustrates a detailed schematic cross-section view of theembodiment of the invention shown in FIG. 18.

FIG. 20 illustrates a schematic cross-section view of an embodiment ofthe invention in which the target is mounted within the vacuum chamberand x-rays are generated using linear accumulation.

FIG. 21 illustrates a detailed schematic cross-section view of theembodiment of the invention shown in FIG. 20.

FIG. 22 illustrates a schematic cross-section view of an embodiment ofthe invention in which two electron beams bombard the target from bothsides.

FIG. 23 illustrates a detailed schematic cross-section view of theembodiment of the invention shown in FIG. 22.

FIG. 24 illustrates a perspective view of a target comprising a grid ofembedded rectangular target microstructures on a larger substrate thatmay be used in some embodiments of the invention.

FIG. 25 illustrates a perspective view of a variation of a targetcomprising a grid of embedded rectangular target microstructures on alarger substrate for use with focused electron beam that may be used insome embodiments of the invention.

FIG. 26A illustrates a perspective view of a target comprising a grid ofembedded rectangular target microstructures as used in some embodimentsof the invention.

FIG. 26B illustrates a top view of the target of FIG. 26A.

FIG. 26C illustrates a side/cross-section view of the target of FIGS.26A and 26B.

FIG. 27A illustrates a perspective view of a target comprising a set ofembedded rectangular target microstructures forming a periodic linearpattern as used in some embodiments of the invention.

FIG. 27B illustrates a top view of the target of FIG. 27A.

FIG. 27C illustrates a side/cross-section view of the target of FIGS.27A and 27B.

FIG. 28 illustrates variations in target structure for a target as shownin FIG. 26 that may arise from processing variations.

FIG. 29 illustrates variations in target structure for a target as shownin FIG. 27 that may arise from processing variations.

FIG. 30 illustrates a cross-section view of a portion of the target ofFIG. 26, showing thermal transfer to a thermally conducting substrateunder electron beam exposure according to the invention.

FIG. 31 illustrates a cross-section view of a variation of the target ofFIGS. 26 and 30 comprising a substrate with a thermal cooling channelaccording to the invention.

FIG. 32 illustrates a cross-section view of another variation of thetarget of FIG. 26 comprising an adhesion layer according to theinvention.

FIG. 33 illustrates a cross-section view of another variation of thetarget of FIG. 26 comprising an electrically conducting overcoataccording to the invention.

FIG. 34 illustrates a cross-section view of another variation of thetarget of FIG. 26 comprising buried x-ray material according to theinvention.

FIG. 35 illustrates a cross-section view of another variation of thetarget of FIG. 26 comprising buried x-ray material and a thick thermallyand electrically conducting overcoat according to the invention.

FIG. 36 illustrates a cross-section view of another variation of thetarget of FIG. 26 comprising an additional blocking structures on theback surface of the substrate, to block the transmission of x-raysproduced by the substrate.

FIG. 37 illustrates a plot of the x-ray absorption of gold and siliconas a function of x-ray energy.

FIG. 38 illustrates a possible structure of an x-ray phase gratingaccording to some embodiments of the invention.

FIG. 39 illustrates a possible structure of an x-ray absorption gratingaccording to some embodiments of the invention.

Note: The illustrations in the Drawings disclosed in this Applicationare typically not shown to scale, and are meant to illustrate theprinciple of the invention and its function only, and not specificrelationships between the microstructures in the target and the variousgrating periods p₁, p₂ and p₃. Please refer to the descriptions in thetext of the Specification for specific details of the dimensions ofthese objects.

DETAILED DESCRIPTIONS OF EMBODIMENTS OF THE INVENTION 1. Descriptions ofVarious Embodiments of the Invention

One embodiment of the invention disclosed herein is an x-rayphase-contrast imaging (XPCI) system as illustrated in FIG. 9. Thesystem bears some similarity to the prior art Talbot-Lau interferometer,in that it comprises a beam splitting grating G₁ 210 of period p₁ thatestablishes a Talbot interference pattern, and an x-ray detector 290typically comprising an array of sensors to convert two-dimensionalx-ray intensities into electronic signals. The beam splitting grating G₁210 may be a phase grating or a transmission grating, and may comprise1-D periodic patterns (linear gratings), or may comprise more complex2-D structures such as a grid that is periodic in two orthogonaldirections. The system may also comprise an analyzer grating G₂ 220 ofperiod p₂ that may be placed in front of the detector to form additionalinterference fringes, such as Moiré fringes. The system may additionallycomprise a means 225 to translate the analyzer grating G₂ 220 relativeto the detector, and a connector 291 to transmit electronic signalscorresponding to the detected x-ray intensity to an image processingsystem 295 for processing.

However, instead of using an extended x-ray source and an additionalgrating G₀ to create a plurality of x-ray source spots, as was done inthe Talbot-Lau system, the embodiments of the present invention use anx-ray source comprising a plurality of x-ray generating sub-sources 108arranged in a periodic array that generate x-rays 188 from electron beambombardment, such that each sub-source is individually coherent, buttogether function as a set of mutually incoherent or partially coherentsub-sources of illumination for the beam splitting grating G₁. As withthe combination of the extended x-ray source and the source grating ofthe Talbot-Lau interferometer, these sub-sources 108 form the Talbotinterference fringe patterns that are created by the beam splittinggrating G₁ 210 and perturbed by an object 240-M, and may be recorded bydetector 290. If the spatial resolution of the detector 290 has aspatial resolution equal to or better than one third of the Talbotfringe period, the detector may record the fringes directly. If a lowerresolution detector is used, an analyzer grating G₂ 220 may also be usedto create Moiré fringes, as was described for the Talbot-Lauinterferometer.

The plurality of discrete x-ray sub-sources can be considerably brighterthan the x-ray source of the Talbot-Lau system. Because the sourcecomprises sub-sources that are self-coherent but may be mutuallyincoherent, there is no need for an attenuating transmission grating G₀to create an array of sub-sources from an extended x-ray source.

A system according to the invention comprising multiple sub-sources in astructured target may be designated a Talbot-ST interferometer.

FIGS. 10, 11 and 12 show a more detailed illustration of one embodimentof the invention, in which the array of sub-sources are formed usingmicrostructures of x-ray generating material embedded in a thermallyconducting substrate. In this embodiment, an x-ray source 008illuminates an object 240-M and a beam-splitting grating G₁ 210, and theinterference pattern they form is detected by a detector 290.

For the x-ray source 008, a high voltage power supply 010 provideselectrons through a lead 021 to an electron emitter 011 in a vacuumchamber 002 held to a shielding housing 005 by supports 003. Theelectron emitter 011 emits electrons 111 towards a target 100. Thetarget 100 comprises a substrate 1000 and a region that comprises aperiodic array of discrete microstructures 700 comprising x-raygenerating material (typically a high Z metallic material such ascopper, molybdenum or tungsten) positioned on or embedded or buried inthe substrate (typically a low Z material such as beryllium, diamond,silicon carbide). The discrete microstructures 700 may be any number ofsizes or shapes, but are generally designed to be periodic arrays ofright rectangular prisms with lateral dimensions on the order of micronsin size in at least one dimension, such that the emission from eachmicrostructure acts as a sub-source of x-rays with a spatial coherencelength that is comparable to or larger than the grating period p₁ at thebeam splitting grating G₁ 210. Additionally, the microstructures arepreferably of a thickness (as typically measured orthogonal to thetarget surface) that is on the order of one half of the electronpenetration depth within the substrate material.

The period p₀ of the microstructures 700 that form the x-ray sub-sourcesis related to the other geometric parameters in the system by:

$\begin{matrix}{p_{0} = {p_{2}\frac{L}{D}}} & \left\lbrack {{Eqn}.\mspace{14mu} 4} \right\rbrack\end{matrix}$where L is the distance from the x-ray sub-sources 700 to the grating G₁210, and D is the distance from the grating G₁ to the detector/analyzergrating G₂ 220 with period p₂. In some embodiments, D will be set to beone of the fractional Talbot distances with interference fringes of highcontrast (visibility), defined by:

$\begin{matrix}{{Contrast} = \frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}} & \left\lbrack {{Eqn}.\mspace{14mu} 5} \right\rbrack\end{matrix}$where I_(max) and I_(min) is the intensity peak and valley of the Talbotinterference fringes without an object in the beam path, respectively.

For plane wave illumination (i.e. equivalent to the x-ray source beinglocated at infinity) of a beam-splitting grating with a π phase-shift,the distance D is preferably given by:

$\begin{matrix}{D = {D_{N} = {{N\frac{p_{1}^{2}}{8\lambda}} = {\frac{N}{16}D_{T}}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 6} \right\rbrack\end{matrix}$where D_(N) is the fractional Talbot distance for a plane waveillumination, λ is the mean x-ray wavelength, and N is referred to as aTalbot fractional order. The preferred value of D is dependent on theattenuating or phase shifting properties of the beam-splitting gratingG₁, the line-space ratio of the beam-splitting grating G₁, and thesource-to-grating distance L. For a π phase-shifting grating with aline-to-space ratio of 1:1, an odd integer fractional Talbot order N(N=1, 3, 5 . . . ) is preferred for determining the distance D. For anx-ray source located at a finite distance (e.g. L not infinity), D isincreased to:

$\begin{matrix}{D = \frac{L \times D_{N}}{L - D_{N}}} & \left\lbrack {{Eqn}.\mspace{14mu} 7} \right\rbrack\end{matrix}$

The Talbot fringe period p_(f) for a given fractional order is given by:

$\begin{matrix}{p_{f} = {K\mspace{14mu} p_{1}\frac{L + D}{L}}} & \left\lbrack {{Eqn}.\mspace{14mu} 8} \right\rbrack\end{matrix}$where K is a parameter dependent on the attenuating or phase shiftingproperties of the beam-splitting grating G₁. K equals 0.5 when thebeam-splitting grating is a π phase-shift grating, and equals 1 when thebeam splitting grating is a π/2 phase shift grating.

Likewise, the Talbot fringe contrast is improved if a smaller x-raysub-source size (i.e. more spatially coherent x-rays) is used, and inwhich the pitch p₁ used for the beam splitting grating G₁ is related tothe size of the sub-source a and the distance L between them, satisfyingthe following requirement:

$\begin{matrix}{p_{1} < \frac{\lambda\; L}{a}} & \left\lbrack {{Eqn}.\mspace{14mu} 9} \right\rbrack\end{matrix}$where λ is a predetermined x-ray wavelength that will generallycorrespond to the wavelength of the monochromatic x-rays produced by thecorresponding sub-source, or the mean x-ray wavelength for an x-raysub-source with a broader spectrum.

In the vacuum chamber 002, electrons 111 bombard the target, andgenerate heat and x-rays 888 in the microstructures 700. The material inthe substrate 1000 is selected such that it has relatively low energydeposition rate for electrons in comparison to the microstructures ofthe x-ray generating material, typically by selecting a low Z materialfor the substrate, and therefore will not generate a significant amountof heat and x-rays. The substrate 1000 material may also be chosen tohave a high thermal conductivity, typically larger than 100 W/(m ° C.).The microstructures of the x-ray generating material are also typicallyembedded within the substrate, i.e. if the microstructures are shaped asrectangular prisms, it is preferred that at least five of the six sidesare in close thermal contact with the substrate 1000, so that heatgenerated in the microstructures 700 is effectively conducted away intothe substrate 1000. However, targets used in other embodiments may havefewer direct contact surfaces. In general, when the term “embedded” isused in this disclosure, at least half of the surface area of themicrostructure will be in close thermal contact with the substrate.

The microstructures are typically connected electrically with a lead 022to the positive terminal of the high voltage source 010 to allow thetarget to serve as an anode in the electrical system. Alternatively, thetarget may be grounded while the cathode (electron emitter) is ofnegative charge, or the target may be connected to a positive terminalwhile the cathode is grounded, so long as the anode is of relativehigher voltage than the cathode. Additionally, in some embodiments,electron optics such as electrostatic lenses or magnetic coils may beplaced inside or outside of the vacuum chamber 002 around or near thepath of electrons 111 to further direct and focus the electron beam.

The target 100 as illustrated may additionally serve as a window in thevacuum chamber 002 so that the x-ray generating material is facing theinterior of the vacuum chamber and the electron source, but x-rays 888are also propagate through the back side of the target 100 towards thebeam-splitting grating G₁ 210. In other embodiments, a separate windowis used, and additional x-ray filters may also be used

Once generated by the source 008, the x-rays 888 may pass through anoptional shutter 230, an x-ray spectral filter to obtain a desiredspectral bandwidth with a desired wavelength, and an object 240-M to beinvestigated. The x-rays then diffract off the beam splitting grating G₁210, which may additionally be mounted on a substrate 211, and then fallon the analyzer grating G₂ 220, which may also be mounted on a substrate221. The final interference pattern will be detected by an arraydetector 290 that provides electrical signals corresponding to the x-rayintensity through a connector 291 to an image processing system 295 foranalysis.

In addition to the x-ray source and interference detection system, meansto move the object 240-M and the various gratings relative to eachother, to the detector, and to the source may be used. In FIG. 10, theimage processing system 295 may also be connected through a network 231to a means 245 of controlling a stage 244 that sets the position andangle of the object 240-M, to a means 215 of controlling a mount 214that sets the position and angle of the beam splitting grating G₁ 210,and to a means 225 of controlling a mount 224 that sets the position andangle of the analyzer grating G₂ 220, as well as a possible connectionto the shutter 230 or to a switch 013 for the high voltage supply 010 toallow the x-rays to be moved and modulated (such as being turned on andoff). Software run by processors in the image processing system 295 maycontrol the motion of the gratings G₁ 210, G₂ 220, the object 240-M, andalso the x-ray exposure to allow the collection of the multiple imagesneeded to obtain detailed amplitude, differential phase, phase-contrast,and scattering contrast images of the object 240-M.

Additional embodiments may also include controls that allow the electronbeam to be moved or modulated. For example, embodiments may be designedthat additionally comprise a means of translating the x-ray source anoderelative to the analyzer grating G₂. Additional embodiments that alsoallow the position and angle of the x-ray detector 290 to be adjustedmay also be designed.

FIG. 13 illustrates an embodiment of the invention in which the target100 comprises a substrate 1000 and a plurality of microstructured linesources 701. These microstructured line sub-sources 701 will typicallybe a few microns wide in one direction (corresponding to the sub-sourcesize parameter a, generally in the dimension orthogonal to the directionof the lines of the gratings G₁ 210 and G₂ 220, which corresponds to they-direction in FIG. 13) but much longer (e.g. up to 1000 microns) in thedirection parallel to the lines (which corresponds to the x-direction inFIG. 13). The pitch of the microstructures 701 as sub-sources as shownin FIG. 13 is p₀, and is related to the pitch of the analyzer/detectorby Equation 4.

FIG. 14 illustrates an embodiment of the invention in which the object240-M to be examined is placed between the gratings G₁ 210 and thedetector 290. The microstructures 700 of x-ray generating material onthe target as illustrated in FIG. 14 comprise sub-sources arranged in a2-D periodic array in two orthogonal directions, but may be any periodicarray that satisfies the coherence illumination condition of thebeam-splitting grating G₁ 210, including a grid, a mesh, a checkerboard,or other periodic structures.

If the gratings comprise one-dimensional structures, the microstructures700 in the source target 100 need only be periodic in the same directionas the 1-D arrays of G₁ 210 and G₂ 220 (i.e. the lines ofmicrostructures 701 are ideally parallel to the lines of the gratings)but can have arbitrary or non-periodic structure in the perpendiculardirection.

FIG. 15 additionally illustrates an embodiment of the invention in whichthe there is no analyzer grating G₂ 220, but instead the detector 299has a high resolution array G_(D) with a pixel resolution equal to orbetter than one third (⅓) of the Talbot fringe period in the directionorthogonal to the grating lines. With this resolution, a single exposureimage may be processed to obtain absorption, phase, and scatteringcontrast images simultaneously. This can be advantageous in that theintensity loss of 50% or more that typically occurs for x-rays passingthrough G₂ 220 is avoided, and the signal reaching the detector andtherefore the signal-to-noise ratio is substantially higher.

In order to collect the multiple images for the calculation of detailedamplitude, differential phase, phase-contrast, and scattering contrastimages for an object 240-M, the embodiment of FIG. 15 may additionallycomprise a means 255 for translating the detector 290, not only in thetwo lateral directions parallel to the plane of the grating G₁, but alsoin direction defined along the path of x-ray propagation, to ensure thatthe detector 299 is placed at the correct multiple of the Talbotdistance T_(D).

FIG. 16 illustrates an embodiment of the invention in which the beamsplitting grating G₁ 210-2D comprises a two-dimensional periodic array,which may be either a transmission or a phase grating. When using a 2-Dbeam-splitting grating of this type, the patterns may be arranged in anyone of a number of periodic patterns, including a mesh, a checkerboard,a circular 2-D array, or other periodic arrays.

FIG. 16 illustrates the use of a 2-D beam splitting grating G₁ 210-2D inconjunction with a high-resolution detector 299, as was also shown inFIG. 15. To simultaneously obtain a differential phase contrast, phasecontrast, absorption, scattering contrast images in two orthogonaldirections, the geometric parameters, including the x-ray sub-sourcesize a, the period p₁ of the grating G₁ 210-2D and the distance L, needto satisfy the coherence illumination condition of the grating G₁ inboth directions. As before, the detector 299 has spatial resolutionequal to or better than ⅓ of the Talbot fringe period in the twoorthogonal directions in the image plane and is positioned to be alignedwith the Talbot fringe pattern.

Such embodiments with 2-D patterns on the beam splitting grating G₁210-2D may also be used with the previously described lower resolutiondetector 290 in conjunction with a two-dimensional analyzer grating G₂which may be phase stepped in two directions in any sequence so that thephase information is obtained in both orthogonal directions. Similar tothe description of G₁ 210-2D above, this 2-D analyzer grating G₂ may beof any periodic structure such as a mesh, a checkerboard, or 2-D arrayof structures such as circles, triangles, squares, rectangles, etc.

FIG. 17 represents an embodiment similar to FIG. 16, except that theobject 240-M under examination is now placed between the x-ray sourceand the beam-splitting grating 210-2D.

Note that some of the embodiments are one-dimensional Talbot-Yuninterferometers in which absorption, phase, and scattering informationis obtained in one direction and incorporate one or more 1-D gratings incombination with a micro structured source target that is periodic in atleast in the direction perpendicular to the grating line direction (butmay be periodic in other directions as well). Other embodiments aretwo-dimensional Talbot-ST interferometers in which absorption, phase,and scattering information is obtained in two orthogonal directions (orall three dimensions by performing computed tomography using the 2-DTalbot-Yun setup).

FIGS. 18 and 19 illustrate another embodiment of the invention in whichthe x-ray source 080 comprises a vacuum chamber 020 supported on mounts030 within an x-ray shielding housing 050. The source 080 also comprisesa target 100 comprising a substrate 1000 and a periodic patterncomprising x-ray sub-sources 700 mounted entirely within the vacuumchamber 020. As before, this embodiment also comprises a high voltagesource 010, which has a negative terminal connected through a lead 021-Ato an electron emitter 011-A, while the positive terminal is connectedthrough one or more leads 022 to the microstructures in the target,allowing them to serve as an anode.

However, in this embodiment, the surface of the target 100 comprisingthe periodic array of x-ray sub-sources 700 comprising of x-raygenerating material is facing a window 040 mounted in the wall of thevacuum chamber 020, and the electron emitter 011-A is aligned to emit abeam of electrons 111-A onto the surface of the target 100 comprisingsub-sources 700 facing the window 040.

FIGS. 20 and 21 illustrate another embodiment of the invention in whichthe target 100 comprising a substrate 1000 and a periodic patterncomprising x-ray sub-sources 700 mounted entirely within the vacuumchamber 020. As before, this embodiment also comprises a high voltagesource 010, which has a negative terminal connected through a lead 021-Bto an electron emitter 011-B, while the positive terminal is connectedthrough one or more leads 022 to the microstructures in the target,allowing them to serve as an anode.

However, in this embodiment, the surface of the target 100 comprisingthe periodic array of x-ray sub-sources 700 comprising x-ray generatingmaterial is oriented such that x-rays produced by some of themicrostructures propagate towards other microstructures that are alsoproducing x-rays, and a linear accumulation of x-rays 888-B from aplurality of microstructures 700 emerges from the target. The distance gbetween the microstructures and microstructures 700 emerges from thetarget. The distance g between the microstructures and the width w_(x)in the propagation direction should be small enough such that theemission from the nth microstructure contributing to the accumulatedx-rays can be considered as a single sub-source with dimension a of Eqn.9, i.e.:a≥tan θ·(n(g+w _(x)))  [Eqn. 10]where a is the sub-source dimension that meets the coherencerequirements of the system, and θ is one half of the field-of-view anglefor the system.

Linear accumulation of x-ray sources as used in this embodiment of theinvention is described more fully in the co-pending U.S. PatentApplication entitled X-RAY SOURCES USING LINEAR ACCUMULATION by theinventors of the present invention (U.S. patent application Ser. No.14/490,672 filed Sep. 19, 2014), which is hereby incorporated byreference in its entirety. Any of the source designs and configurationsdisclosed in the above referenced co-pending Application may beconsidered for use as a component in any or all of the interferometricimaging systems disclosed herein.

Likewise, FIGS. 22 and 23 illustrate another embodiment of the inventionthat utilizes linear accumulation of x-rays. In this embodiment, thex-ray source 080 includes a target 2200 comprising a substrate 2210 anda first set of sub-sources 707 and a second set of sub-sources 708mounted entirely within the vacuum chamber 020. As before, thisembodiment also comprises a high voltage source 010, but this highvoltage source is connected to a junction 010-2 that provides highvoltage to two electron emitters 011-D and 011-E through a leads 021-Dand 021-E, respectively. As shown in FIGS. 22 and 23, the first electronemitter 021-D provides an electron beam 111-D that bombards the firstset of sub-sources 707, while the second electron emitter 021-E providesan electron beam 111-E that bombards the second set of sub-sources 708.Some of the x-rays 788 generated by the first set of sub-sources 707 andthe second set of sub-sources 708 along the x-ray imaging beam axiscombine to produce x-rays 2888 from the target 2200 will be augmented bythe linear accumulation of x-rays from these two sets of x-raysub-sources.

It will also be known to those skilled in the art that other embodimentsof the invention comprising an x-ray source in which the target/anodeunder bombardment by electrons is moved, translated, or rotated todistribute the heat load are also possible.

Note: The illustrations of FIGS. 10 through 23 are not shown to scale,and are meant to illustrate the principle of the invention and notspecific relationships between the microstructures 700, the target 100and the various grating periods p₁ and p₂. The microstructures 700, 701,707, 708 etc. may be on the order of microns in size, while the objectunder examination 240-M may be centimeters in size. Likewise, althoughthese are illustrated in which an object with dimensions on the order ofcentimeters (a mouse) is shown, the techniques described are not limitedto such objects, but may be used to examine even larger structures, ormicroscopic structures as well, as long as a suitable resolution for thedetector and other elements of the interferometer are suitablyconstructed.

2. Fabrication of X-Ray Targets

Targets such as those to be used in x-ray sources according to theinvention disclosed herein have been described in detail in theco-pending U.S. Patent Application entitled STRUCTURED TARGETS FOR X-RAYGENERATION by the inventors of the present invention (U.S. patentapplication Ser. No. 14/465,816, filed Aug. 21, 2014), which is herebyincorporated by reference in its entirety. Any of the target designs andconfigurations disclosed in the above referenced co-pending Applicationmay be considered for use as a component in any or all of the x-raysources disclosed herein.

As described herein and in the above cited pending Patent Applications,the target used in the source of x-rays may comprise a periodic array ofsub-sources. Each sub-source may be comprised of a single or multiplemicrostructures of x-ray generating material in thermal contact with, orpreferably embedded in, a substrate selected for its thermalconductivity. When the microstructures are in good thermal contact witha substrate having a high thermal conductivity, higher electron currentdensities may be used to generate x-rays, since the excess heat will bedrawn away into the substrate. The higher current densities will giverise to higher x-ray flux, leading to a higher brightness source. Asdescribed in the above co-pending patent Applications, sources withmicrostructures of x-ray generating material may have a brightness morethan 10 times larger than simpler constructions made from the samematerials. Additional configurations in which multiple sub-sources arealigned to contribute x-rays on the same axis can multiply thebrightness further through linear accumulation of the x-ray sub-sources.

It should also be noted here that, when the word “microstructure” isused herein, it is specifically referring to microstructures comprisingx-ray generating material. Other structures, such as the cavities usedto form the x-ray microstructures, have dimensions of the same order ofmagnitude, and might also be considered “microstructures”. As usedherein, however, other words, such as “structures”, “cavities”, “holes”,“apertures”, etc. may be used for these structures when they are formedin materials, such as the substrate, that are not selected for theirx-ray generating properties. The word “microstructure” will be reservedfor structures comprising materials selected for their x-ray generatingproperties.

Likewise, it should be noted that, although the word “microstructure” isused, x-ray generating structures with dimensions smaller than 1 micron,or even as small as nano-scale dimensions (i.e. greater than 10 nm) mayalso be described by the word “microstructures” as used herein as longas the properties are consistent with the geometric factors forsub-source size and grating pitches set forth in the variousembodiments.

It should also be noted that here that, when the word “sub-source” isused it may refer to a single microstructure of x-ray generatingmaterial, or an ensemble of smaller microstructures that functionsimilarly to a single structure for the purposes of Talbotinterferometry.

The fabrication of these microstructured targets may follow well knownprocessing steps used for the creation of embedded structures insubstrates. If the substrate is a material with high thermalconductivity such as diamond, conventional lithographic patterning usingphotoresists can produce micron sized structures, which may then beetched into the substrate using processes such as reactive ion etching(RIE). Deposition of the x-ray generating material into the etchedstructures formed in the substrate may then be carried out usingstandard deposition processes, such as electroplating, chemical vapordeposition (CVD), or atomic layer deposition.

The x-ray generating material used in the target should ideally havegood thermal properties, such as a high melting point and high thermalconductivity, in order to allow higher electron power loading on thesource to increase x-ray production. The x-ray generating materialshould additionally be selected for good x-ray production properties,which includes x-ray production efficiency (proportional to its atomicnumber) and in some cases, it may be desirable to produce a specificspectra of interest, such as a characteristic x-ray spectral line. Forthese reasons, targets are often fabricated using tungsten, with anatomic number Z=74.

Table I lists several materials that are commonly used for x-raytargets, several additional potential target materials (notably usefulfor specific characteristic lines of

TABLE I Various Target and Substrate Materials and Selected Properties.Atomic Melting Thermal Electrical Material Number Point ° C.Conductivity Conductivity (Elemental Symbol) Z (1 atm) (W/(m ° C.))(MS/m) Common Target Materials: Chromium (Cr) 24 1907 93.7 7.9 Iron (Fe)26 1538 80.2 10.0 Cobalt (Co) 27 1495 100 17.9 Copper (Cu) 29 1085 40158.0 Molybdenum (Mo) 42 2623 138 18.1 Silver (Ag) 47 962 429 61.4Tungsten (W) 74 3422 174 18.4 Other Possible Target Materials: Titanium(Ti) 22 1668 21.9 2.6 Gallium (Ga) 35 30 40.6 7.4 Rhodium (Rh) 45 1964150 23.3 Indium (In) 49 157 81.6 12.5 Cesium (Cs) 55 28 35.9 4.8 Rhenium(Re) 75 3185 47.9 5.8 Gold (Au) 79 1064 317 44.0 Lead (Pb) 82 327 35.34.7 Other Potential Substrate Materials with low atomic number:Beryllium (Be) 4 1287 200 26.6 Carbon (C): Diamond 6 * 2300 10⁻¹⁹ Carbon(C): Graphite ∥ 6 * 1950 0.25 Carbon (C): 6 * 3180 100.0 Nanotube (SWNT)Carbon (C): 6 * 200 Nanotube (bulk) Boron Nitride (BN) B = 5 ** 20 10⁻¹⁷N = 7 Silicon (Si) 14 1414 124 1.56 × 10⁻⁹ Silicon Carbide Si = 14 27980.49 10⁻⁹  (β-SiC) C = 6 Sapphire (Al₂O₃) ∥ C Al = 13 2053 32.5 10⁻²⁰ O= 8 * Carbon does not melt at 1 atm; it sublimes at ~3600° C. ** BN doesnot melt at 1 atm; it sublimes at ~2973° C.interest), and some materials that may be used as substrates for targetmaterials. Melting points, and thermal and electrical conductivities arepresented for values near 300° K (27° C.). Most values are cited fromthe CRC Handbook of Chemistry and Physics, 90^(th) ed. [CRC Press, BocaRaton, Fla., 2009]. Other values are cited from various sources found onthe Internet. Note that, for some materials, such as sapphire forexample, thermal conductivities an order of magnitude larger may bepossible when cooled to temperatures below that of liquid nitrogen (77°K) [see, for example, Section 2.1.5, Thermal Properties, of E. R.Dobrovinskaya et al., Sapphire: Material, Manufacturing, Applications,Springer Science+Business Media, LLC, 2009].

FIG. 24 illustrates a target as may be used in some embodiments of theinvention. In this figure, a substrate 1000 has a region 1001 thatcomprises an array of sub-sources 700 comprising microstructures ofx-ray generating material (typically a metallic material), in which thesub-sources are arranged in a regular array of right rectangular prisms.In a vacuum, electrons 111 bombard the target from above, and generateheat and x-rays in the microstructures 700. The material in thesubstrate 1000 is selected such that it has relatively low x-rayproduction (efficiency is proportional to atomic number) and energydeposition rate (stopping power is proportional to density) forelectrons in comparison to the x-ray generating microstructure material,and therefore will not generate a significant amount of heat and x-rays.This is typically achieved by selecting a low mass density and lowatomic number (Z) material for the substrate.

The substrate 1000 material may also be chosen to have a high thermalconductivity, typically larger than 100 W/(m ° C.), and themicrostructures are typically embedded within the substrate, i.e. if themicrostructures are shaped as rectangular prisms, it is preferred thatat least five of the six sides are in close thermal contact with thesubstrate 1000, so that heat generated in the microstructures 700 iseffectively conducted away into the substrate 1000. However, targetsused in other embodiments may have fewer direct contact surfaces. Ingeneral, when the term “embedded” is used in this disclosure, at leasthalf of the surface area of the microstructure will be in close thermalcontact with the substrate.

Note that the sub-source sizes and dimensions in some embodiments may beconstrained by the same limitations as the periodicity p₀ of the gratingG₀ in prior art. In other words, the spatial resolution achievable atthe object position in the x-ray interferometric imaging systems asshown in FIGS. 9 through 23 is determined by the overall x-ray sourcesize and the detector resolution, similar to the conditions described inthe prior art interferometeric imaging systems, such as the Talbot-Lausystem. Therefore, the maximum x-ray source size (width of eachmicrostructure spot) is limited for a given detector resolution and agiven imaging geometry as determined by the distance between the sourceand object and the distance between the object to the detector.

The line-to-space ratio of the arrays of sub-sources is a designparameter that should be considered in the design of any system. A largespatial coherence length is inversely proportional to the size of anx-ray source or sub-source. Because the fringe visibility of the Talbotinterference fringes increases linearly with the relative ratio of thespatial coherence length of the illuminating x-ray beam to the period ofthe beam-splitting grating p₁ for a value of the ratio from 0.3 to 1, itis generally preferred to have a small source size. However, the x-rayproduction is inversely proportional to the area of the sub-source (e.g.a reduction in line width will lead to a decrease of x-ray production).Since the throughput of an imaging system is generally proportional tosquare of the contrast transfer function and only proportional to thex-ray flux, it is generally preferred to have a line-to-space rationless than 1:1. Some embodiments of the invention may use a line-to-space(i.e. x-ray generating material to substrate material) ratio between 1:5and 1:2 (i.e. the relative area of the x-ray generating material mayrange from 20% to 33%).

A figure of merit (FOM) that may be helpful for the selection ofmaterials for targets according to this invention is the ratio of x-raysproduced by the microstructures to the x-rays produced by the electronsalso bombarding the substrate. This figure of merit may be useful forthe design of and selection of materials for the targets for the system,and should be taken into consideration in addition to the thermalconductivity of the substrate. As the electron energy deposition rate isproportional to the mass density and the x-ray production efficiency ina material is proportional to its atomic number, this figure of meritmay be defined as follows:

$\begin{matrix}{{FOM} = \frac{Z_{2} \times \rho_{2}}{Z_{1} \times \rho_{1}}} & \left\lbrack {{Eqn}.\mspace{14mu} 11} \right\rbrack\end{matrix}$where Z is the atomic number and ρ is the density, and material 1 is thesubstrate and material 2 is the x-ray generating material.

A number of microstructures and substrate material combinations arelisted below in Table II. Any of the following combinations may be used,but it is preferable that the materials are selected such that the FOMis greater than 12, and that the thermal conductivity of the substratematerial is greater than 100 W/(m ° C.) at room temperature.

TABLE II Figure of Merit for x-ray material/substrate combinations.Substrate material Microstructure material Figure Mass Mass of MeritAtomic # density Atomic # density Z₂ × ρ₂ Material Z₁ (g/cm³) MaterialZ₂ (g/cm³) Z₁ × ρ₁ SiC 12.55 3.21 Cu 29 8.96 6 Si 14 2.33 Cu 29 8.96 8SiC 12.55 3.21 Mo 42 10.2 11 Diamond 6 3.5 Cu 29 8.96 12 Si 14 2.33 Mo42 10.2 13 Diamond 6 3.5 Mo 42 10.2 21 SiC 12.55 3.21 W 74 19.25 35 Be 41.85 Cu 29 8.96 35 Si 14 2.33 W 74 19.25 44 Be 4 1.85 Mo 42 10.2 59Diamond 6 3.5 W 74 19.25 68 Be 4 1.85 W 74 19.25 193

FIG. 25 illustrates another target as may be used in some embodiments ofthe invention in which the electron beam 111-F is directed byelectrostatic lenses to form a more concentrated, focused spot. For thissituation, the target 1100-F will still comprise a region 1001-Fcomprising an array of microstructures 700-F comprising x-ray material,but the size and dimensions of this region 1001-F can be matched toregions where electron exposure will occur. In these targets, the“tuning” of the source geometry and the x-ray generating material can becontrolled such that the designs mostly limit the amount of heatgenerated to the microstructured region 1001-F, while also reducing thedesign and manufacturing complexity. This may be especially useful whenused with electron beams focused to form a micro-spot, or by moreintricate systems that form a more complex electron exposure pattern.

The depth of penetration of electrons into the material can be estimatedby Pott's Law [P. J. Potts, Electron Probe Microanalysis, Ch. 10 of AHandbook of Silicate Rock Analysis, Springer Netherlands, 1987, p.336)], which states that the penetration depth x in microns is relatedto the 10% of the value of the electron energy E₀ in keV raised to the3/2 power, divided by the density of the material:

$\begin{matrix}{{x({µm})} = {0.1 \times \frac{E_{0}^{1.5}}{\rho}}} & \left\lbrack {{Eqn}.\mspace{14mu} 12} \right\rbrack\end{matrix}$For less dense material, such as a diamond substrate, the penetrationdepth is much larger than for a material with greater density, such asmost materials containing elements used for x-ray generation.

Using this formula, Table III illustrates some of the estimatedpenetration depths for some common x-ray target materials.

TABLE III Estimates of penetration depth for 60 keV electrons into somematerials. Density Penetration Depth Material Z (g/cm³) (μm) Diamond 63.5 13.28 Copper 29 8.96 5.19 Molybdenum 42 10.28 4.52 Tungsten 74 19.252.41

The majority of characteristic Cu K x-rays are generated within thepenetration depth. The electron interactions below that depth typicallygenerate few characteristic K-line x-rays but will contribute to theheat generation, thus resulting in a low thermal gradient along thedepth direction. It is therefore preferable in some embodiments to set amaximum thickness for the microstructures in the target in order tolimit electron interaction in the material and optimize local thermalgradients. One embodiment of the invention limits the depth of the microstructured x-ray generating material in the target to between one thirdand two thirds of the electron penetration depth in the substrate at theincident electron energy. In this case, the lower mass density of thesubstrate leads to a lower energy deposition rate in the substratematerial immediately below the x-ray generating material, which in turnleads to a lower temperature in the substrate material below. Thisresults in a higher thermal gradient between the x-ray generatingmaterial and the substrate, enhancing heat transfer. The thermalgradient is further enhanced by the high thermal conductivity of thesubstrate material.

For similar reasons, selecting the thickness of the microstructures tobe less than one half of the electron penetration depth in the substrateis also generally preferred for efficient generation of bremsstrahlungradiation, because the electrons below that depth have lower energy andthus lower x-ray production efficiency.

Note: Other choices for the dimensions of the x-ray generating materialmay also be used. In targets as used in some embodiments of theinvention, the depth of the x-ray material may be selected to be 50% ofthe electron penetration depth in the substrate. In other embodiments,the depth of the x-ray material may be selected to be 33% of theelectron penetration depth in the substrate. In other embodiments, thedepth for the microstructures may be selected related to the “continuousslowing down approximation” (CSDA) range for electrons in the material.Other depths may be specified depending on the x-ray spectrum desiredand the properties of the selected x-ray material.

FIG. 26 illustrates a region 1001 of a target as may be used in someembodiments of the invention that comprises an array of sub-sources 700with microstructures in the form of right rectangular prisms comprisingx-ray generating material arranged in a regular array. FIG. 26A presentsa perspective view of the sixteen microstructures 700 for this target,while FIG. 26B illustrates a top down view of the same region, and FIG.26C presents a side/cross-section view of the same region. (For the term“side/cross-section view” in this disclosure, the view meant is one asif a cross-section of the object had been made, and then viewed from theside towards the cross-sectioned surface. This shows both detail at thepoint of the cross-section as well as material deeper inside that mightbe seen from the side, assuming the substrate itself were transparent[which, in the case of diamond, is generally true for visible light].)

In these targets, the microstructures have been fabricated such thatthey are in close thermal contact on five of six sides with thesubstrate. As illustrated, the top of the microstructures 700 are flushwith the surface of the substrate, but other targets in which themicrostructure is recessed may be fabricated, and still other targets inwhich the microstructures present a topographical “bump” relative to thesurface of the substrate may also be fabricated.

An alternative target as may be used in some embodiments of theinvention may have several microstructures of right rectangular prismssimply deposited upon the surface of the substrate. In this case, onlythe bottom base of the prism would be in thermal contact with thesubstrate. For a structure comprising the microstructures embedded inthe substrate with a side/cross-section view as shown in FIG. 26C withdepth D_(z) and lateral dimensions in the plane of the substrate ofW_(x) and W_(y), the ratio of the total surface area in contact with thesubstrate for the embedded microstructures vs. deposited microstructuresis

$\begin{matrix}{\frac{A_{Embedded}}{A_{Deposited}} = {1 + {2\; D\frac{\left( {W + L} \right)}{\left( {W \times L} \right)}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 13} \right\rbrack\end{matrix}$With a small value for D relative to W and L, the ratio isessentially 1. For larger thicknesses, the ratio becomes larger, and fora cube (D=W=L) in which 5 equal sides are in thermal contact, the ratiois 5. If a cap layer of a material with similar properties as thesubstrate in terms of mass density and thermal conductivity is used, theratio may be increased to 6.

FIG. 27 illustrates a region 1001 of a target as may be used in someembodiments of the invention, such as that previously illustrated inFIG. 13, that comprises an array of linear sub-sources 701 withmicrostructures in the form of right rectangular prisms comprising x-raygenerating material arranged in a regular array. FIG. 27A presents aperspective view of the three microstructures 701 for this target, whileFIG. 27B illustrates a top down view of the same region, and FIG. 27Cpresents a side/cross-section view of the same region.

In this embodiment, the lateral dimensions in the plane of the substrateare a width and length W_(x) and L_(y). The effective sub-source size awill correspond to the width W_(x).

FIGS. 28 and 29 illustrate a practical issue that may arise in formingthe targets such as those illustrated in FIGS. 26 and 27. FIG. 28illustrates variations possible with the grid of x-ray generatingmicrostructures 700 as illustrated in FIG. 26, and FIG. 29 illustratesvariations possible with the linear x-ray generating microstructures 701as illustrated in FIG. 27.

In FIG. 28, odd-shaped microstructures 700-A of other geometric shapesmay be formed. Likewise, voids 700-O may also appear where certainstructures may be expected. Other deposition processes, for exampledeposition using pre-formed particles of x-ray generating material maycreate ensemble clusters of particles 700-C that, when bombarded withelectrons, may still act as x-ray sub-sources similar in function tothose that are produced by a uniform structure. Also shown in FIG. 28 isa microstructure with multiple crystal structures and grain boundaries700-G that again may still produce x-rays similar to those that areproduced by a uniform structure, but may be considered to comprise anensemble of microstructures.

The effective x-ray sub-source size in all of these situations may beapproximated using the size parameter a, even though the microstructurescomprise particles that are considerable smaller.

In FIG. 29 shows examples of ensemble microstructures as may occur whenfabricating linear microstructures 701. If uniform pre-fabricatedparticles of x-ray generating material are created and coated onto thesubstrate, an ensemble of particles 703 of x-ray generating material maybe formed. In other processes, if non-uniform particles are used,clusters of particles 704-A and 704-B may form, in some cases with anon-uniform distribution that may include gaps of voids. In otherprocesses, an ensemble of particles 704 of x-ray generating material mayapproximate a line source of x-rays.

All of these ensembles, when bombarded with electrons, may still act asx-ray sub-sources similar in function to those that are produced by auniform linear structure. The effective source size in these situationsmay be approximated using the size parameter a, even though themicrostructures comprise particles that are considerable smaller.

The heat transfer that may occur under electron bombardment isillustrated with representative arrows in FIG. 30, in which the heatgenerated in sub-sources 700 embedded in a substrate 1000 is conductedout of the microstructures comprising the sub-sources 700 through thebottom and sides (arrows for transfer through the sides out of the planeof the drawing are not shown). The amount of heat transferred per unittime (ΔQ) conducted through a material of area A and thickness d givenby:

$\begin{matrix}{{\Delta\; Q} = \frac{{\kappa \cdot A \cdot \Delta}\; T}{d}} & \left\lbrack {{Eqn}.\mspace{14mu} 14} \right\rbrack\end{matrix}$where κ is the thermal conductivity in W/(m ° C.) and ΔT is thetemperature difference across thickness d in ° C. Therefore, an increasein surface area A, a decrease in thickness d and an increase in ΔT alllead to a proportional increase in heat transfer.

An alternative embodiment is illustrated in FIG. 31, in which thesubstrate additionally comprises a cooling channel 1200. Such coolingchannels may be a prior art cooling channel, as discussed above, usingwater or some other cooling fluid to conduct heat away from thesubstrate, or may be fabricated according to a design adapted to bestremove heat from the regions near the embedded microstructures 700.

Other target structures for various embodiments may be understood ordevised by those skilled in the art, in which the substrate may, forexample, be bonded to a heat sink, such as a copper block, for improvedthermal transfer. The copper block may in turn have cooling channelswithin it to assist in carrying heat away from the block. Alternatively,the substrate may be attached to a thermoelectric cooler, in which avoltage is applied to a specially constructed semiconductor device. Inthese devices, the flow of current causes one side to cool while theother heats up. Commercially available devices, such as Peltier coolers,can produce a temperature difference of up to 70° C. across the device,but may be limited in their overall capacity to remove large amounts ofheat from a heat source. Heat pipes containing a heat transfer fluidthat evaporates and condenses, as are used for cooling CPU chips inserver farms when compact design is a consideration, may also be used tocool the substrate.

Alternatively, the substrate can be attached to a cryogenic cooler, suchas a block containing channels for the flow of liquid nitrogen, or be inthermal contact with a reservoir of liquid nitrogen or some othercryogenic substance, such as an antifreeze solution, to provide moreextreme cooling. When the substrate comprises a material such asdiamond, sapphire, silicon, or silicon carbide, thermal conductivitygenerally increases with decreasing temperature from room temperature.In such a case, designing the target so that it can withstand cooling tothese lower temperatures may be preferred.

FIG. 32 illustrates an alternative example of a target that may be usedin embodiments of the invention in which the cavities formed in thesubstrate 1000 are first coated with an adhesion layer 715 (preferablyof minimal thickness) before embedding the x-ray generating materialthat forms the microstructures 700. Such an adhesion layer may beappropriate in cases where the bond between the x-ray material and thesubstrate material is weak. The adhesion layer may also act as a bufferlayer when the difference between thermal expansion coefficients for thetwo materials is large. For some choices of materials, the adhesionlayer may be replaced or extended (by adding another layer) with adiffusion barrier layer to prevent the diffusion of material from themicrostructures into the substrate material (or vice versa). Forembodiments in which an adhesion and/or diffusion barrier layer is used,the selection of materials and thicknesses should consider the thermalproperties of the layer as well, such that heat flow from themicrostructures 700 to the substrate 1000 is not significantly impededor insulated by the presence of the adhesion layer 715.

FIG. 33 illustrates an alternative example of a target that may be usedin embodiment in which an electrically conducting layer 725 has beenadded to the surface of the target. When bombarded by electrons, theexcess charge needs a path to return to ground for the target tofunction effectively as an anode. If the target as illustrated in FIG.26 were to comprise only discrete, unconnected microstructures 700within an electrically insulating substrate material (such as undopeddiamond), under continued electron bombardment, significant charge wouldbuild up on the surface. The electrons from the cathode would then notcollide with the target with the same energy, or might even be repelled,diminishing the generation of x-rays.

This can be addressed by the deposition of a thin layer of conductingmaterial that is preferably of relatively low atomic number, such asaluminum (Al), beryllium (Be), carbon (C), chromium (Cr) or titanium(Ti), that allows electrical conduction from the discretemicrostructures 700 to an electrical path 722 that connects to apositive terminal relative to the high voltage supply. This terminal asa practical matter is typically the electrical ground of the system,while the cathode electron source is supplied with a negative highvoltage.

FIG. 34 illustrates another example of a target that may be used inembodiment of the invention, in which the sub-sources 702 are embeddeddeeper, or buried, into the substrate 1000. Such an embeddedmicrostructure may be further covered by the deposition of an additionallayer 1010, which may be, for example, diamond, providing the same heattransfer properties as the substrate. This allows heat to be conductedaway from all sides of the buried sub-source 702. For such a situationand when the additional layer 1010 does not have sufficient electricalconductivity, it is advisable to provide a path 722 to ground for theelectrons incident on the structure, which may be in the form of aembedded conducting layer 726 laid down before the deposition of theadditional layer 1010. In some embodiments, this conducting layer 726will have a “via” 727, or a vertical connection, often in the form of apillar or cylinder, that provides an electrically conducting structureto link the embedded conducting layer 726 to an additional conductinglayer 728 on the surface of the target, which in turn is connected tothe path 722 to ground, or the high voltage supply.

FIG. 35 illustrates another example of a target that may be used inembodiments of the invention, in which the sub-sources 702 are againburied within the substrate. However, in this embodiment, instead offirst providing an electrically conducting layer followed by thedeposition of an additional cap layer, in this embodiment only a singlelayer 770 is deposited, selected for a combination of electricalproperties and thermally conducting properties. This may be, forexample, a deposition of carbon nanotubes (Z=6) oriented verticallyrelative to the surface, such that they conduct both heat and electronsaway from the buried microstructures 702. This single layer 770 may inturn be connected to a path 722 to ground to allow the target to serveas an anode in the x-ray generation system. Alternatively, the materialof the layer 770 may be selected to comprise aluminum (Al), beryllium(Be), chromium (Cr), or copper (Cu).

FIG. 36 illustrates another variation of an embodiment, in which anadditional patterns of blocking material 729 have been deposited on thebackside of the target substrate 1000. If the figure of merit for theselected material combination, as discussed above in Table II, is notlarge, there may still be significant x-rays generated by the substratethat will reduce contrast in the image. These substrate-generated x-rayscan be blocked by a deposition of a suitable material, such as gold, asblocking structures 729. Gold (Z=79) has a strong x-ray absorption, asillustrated in FIG. 37. Processes to deposit these blocking structuresmay comprise standard deposition processes, and an alignment step may beneeded to ensure alignment with the x-ray generating structures on theopposite side.

It should be clear to those skilled in the art that although severalembodiments have been presented separately in FIGS. 24-36, and variousprocesses for their manufacture will be presented later, the elements ofthese embodiments may be combined with each other, or combined withother commonly known target fabrication methods known in the art. Forexample, the buried sub-sources 702 of FIG. 35 may also comprisemultiple grains of microstructures, as was illustrated in FIGS. 28 and29. Likewise, the adhesion layer 715 as illustrated in FIG. 32 may alsobe applied to fabrication of embedded sub-sources 700 as shown in FIG.33. The separation of these alternatives is for illustration only, andis not meant to be limiting for any particular process.

Although the sub-sources illustrated in FIGS. 24-36 have been shown asregularly spaced patterns with uniform size and shape, a regular patternof sub-sources having non-uniform size and shape, can also be used insome embodiments of the invention. Additionally, each sub-source withina regular periodic pattern may further be comprised of multiple smallermicrostructures of non-uniform sizes and shapes. These smallermicrostructures may be non-regular and do not necessarily need to havesimilar x-ray emission characteristics or strength, so as long as thelarger sub-sources that each group of microstructures comprise areperiodic in nature.

Likewise, although some embodiments have been described withmicrostructures in, for example, the shape of right rectangular prisms,fabrication processes may create structures that have walls at anglesother than 90°, or do not have corners that are exactly right angles,but may be rounded or beveled or undercut, depending on the artifacts ofthe specific process used. Embodiments in which the microstructures areessentially similar with the shapes described herein will be understoodby those skilled in the art to be disclosed, even if process artifactslead to some deviation from the shapes as illustrated or described.

In other embodiments of the system, a periodic attenuating grating G₀such as are used in the prior art Talbot-Lau interferometers may also beused in conjunction with the source of the invention, so that the x-raysproduced by the substrate material surrounding the sub-sources arefurther attenuated, allowing greater monochromaticity and thereforehigher spatial coherence for the source. The apertures of the gratingshould be coincident with projections of the microstructured x-raysub-sources, or may, in some embodiments, be placed at a Talbotfractional or integer distance downstream of the source and with theapertures coincident with the source self-images. It is preferable thatthe grating G₀ is of high atomic number and relatively low aspect ratio,for ease of manufacturability.

3. Fabrication of Gratings

Fabrication of the gratings used in embodiments of the invention may bemade using known prior art fabrication processes such as thosepreviously described by Christian David [C. David et al., “Fabricationof diffraction gratings for hard x-ray phase contrast imaging”,Microelectron. Eng. 84, 1172-1177, 2007].

Gratings for x-rays may be fabricated using silicon substrates, withetched changes in topography to induce phase changes and depositions ofa higher Z material, such as gold (Au, Z=79), to induce absorptionchanges. The x-ray absorption properties for gold and silicon areillustrated in FIG. 37.

As shown in FIG. 38, a periodic pattern 3010 may be etched into asilicon substrate 3000 to create a structure which introduces a periodicphase shift for x-rays falling at normal incidence. The phase shiftdepends on the etch depth, with a phase-shift of z radians for normalincidence x-rays achieved when the following condition is met:

$\begin{matrix}{d_{etch} = {{\frac{1}{2}\frac{\lambda}{{n - 1}}} = {\frac{1}{2}\frac{\lambda}{\delta}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 15} \right\rbrack\end{matrix}$

Values for δ for silicon at several x-ray energies, along with the depthetched structures need to a phase-shift of π radians are shown in TableIV.

TABLE IV Etch depth for Silicon phase shift of π radians. X-ray EnergyWavelength π phase shift (keV) λ (nm) δ depth (μm)  3.0 0.413 5.43E−053.81  5.0 0.248 1.98E−05 6.26 8.048 (Cu Kα) 0.154 7.58E−06 10.17 10.00.124 4.89E−06 12.69  17.48 (Mo Kα) 0.0709 1.59E−06 22.36 30.0 0.04135.36E−07 38.52 50.0 0.0248 1.93E−07 64.31 59.39 (W Kα)  0.0209 1.37E−0776.32 100.0  0.0124 4.82E−08 128.74

A typical grating fabrication process comprises coating a <110> orientedsilicon wafer with a photoresist, and patterning the resist usingconventional photolithography or electron beam lithography. The siliconthen undergoes an etching process such as wet etching in, for example, apotassium hydroxide (KOH) solution, or reactive ion etching (RIE), withthe etching selectively occurring only for portions of the silicon notmasked by the resist. The etch depth may be controlled by adjusting thetime of the etch process. Other variations of the etching process willbe known those skilled in the art of semiconductor processing andmanufacturing.

Absorption gratings such as those used for G₂ may be fabricated byinitially crating a silicon phase grating, as described above, and thendepositing an x-ray absorbing material, such as gold, into the groovesalready patterned in the silicon. This is illustrated in FIG. 39, inwhich an amount of x-ray absorbing material 3030 such as gold has filledthe grooves created in a silicon substrate 3000. One process for thedeposition of gold into the silicon grooves involves a standardelectroplating processes. To ensure that gold is only deposited into thegrooves, a sacrificial layer of aluminum may initially deposited at anangle, and a seed layer ˜50 nm thick comprising Chromium (Cr) and gold(Au) are then deposited. A phosphoric acid treatment removes the all thematerial deposited on the tops of the silicon structures, leaving seedmaterial only in the bottom of the grooves in the silicon. Standardelectroplating may follow, with growth of gold occurring only onto thedeposited seed layers. Deposition of 10 to 20 mm of gold can createabsorption gratings with a transmission modulation of 75% or more.Absorption will, however, depend on the x-ray energy and the absorptioncoefficient for the material, as was illustrated in FIGS. 1 and 37.Other methods for making x-ray absorption gratings will be known tothose skilled in the art.

For some applications and for certain x-ray wavelengths, crystalgratings may also be used.

4.0 Detector Properties

The detector may be any one of a number of detectors used to form x-rayimages. One type of commonly used x-ray detector comprises a fluorescentscreen or scintillator, such as one comprising a layer of cesium iodide(CsI), thallium doped CsI, yttrium aluminium garnet (YAG) or gadoliniumsulfoxylate (GOS), that emits visible photons when exposed to x-rays.The visible photons are then detected by an electronic sensor thatconverts visible intensity into electronic signals, often with theadditional formation of a relay image using visible optics that enlargeand magnify the intensity pattern of the photons emitted by thefluorescent screen. With the relay optics, the electronic detector neednot comprise a high resolution sensor itself, and inexpensive commercialCCD detectors or complementary metal-oxide-semiconductor (CMOS) sensorarrays with, for example, 1024×1024 pixels, each 24 μm×24 μm square, maybe used.

Commercial flat panel digital x-ray sensors in which a layer ofscintillator material is placed in close proximity to (or even coatedonto) an array of conventional optical image sensors are manufacturedby, for example, Varian Inc. of Palo Alto, Calif. and General Electric,Inc. of Billerica, Mass. Other configurations of image sensors may beknown to those skilled in the art. In embodiments in which a G2 analyzergrating is used, it is preferable to use highly efficient, fast read-outdetectors such as flat panel detectors, used for medical and industrialuses. For many applications, a flat panel detector with a resolutionlarger than 20 microns will require that an analyzer grating G₂ with aperiod equal to the Talbot fringe period to be placed in the x-ray beampath before the detector.

A second approach is to use an electronic sensor that directly createsan electrical signal in response to the absorption of x-rays, by, forexample, the creation of direct electron-hole pairs in amorphousselenium (a-Se). These are then converted into electronic signals usingan array of thin-film transistors (TFTs). Such direct flat paneldetectors (FPDs) such as the Safire FPD of Shimadzu Corp. of Kyoto,Japan, are commercially available.

5.0 Variations

Embodiments may further comprise other components typically included inTalbot interferometer, including spectral filters to obtain a desiredx-ray energy bandwidth and positioning control systems for all thevarious components of the system.

With this application, several embodiments of the invention, includingthe best mode contemplated by the inventors, have been disclosed. Itwill be recognized that, while specific embodiments may be presented,elements discussed in detail only for some embodiments may also beapplied to others.

While specific materials, designs, configurations and fabrication stepshave been set forth to describe this invention and the preferredembodiments, such descriptions are not intended to be limiting.Modifications and changes may be apparent to those skilled in the art,and it is intended that this invention be limited only by the scope ofthe appended claims.

We claim:
 1. An x-ray interferometric imaging system comprising: asource of x-rays comprising: a vacuum chamber; an electron beam emitter;and a target comprising: a substrate comprising a first material; and aplurality of discrete structures embedded in the substrate, theplurality of discrete structures comprising a second material thatgenerates x-rays in response to electron irradiation, said plurality ofdiscrete structures arranged in a periodic pattern to produce a periodicpattern of sub-sources of x-rays when irradiated by electrons from theelectron beam emitter; a beam-splitting x-ray grating comprisingperiodic structures that introduce a phase shift for a predeterminedx-ray wavelength, the periodic structures comprising two-dimensionalstructures arranged in a checkerboard pattern, said beam-splitting x-raygrating positioned to diffract x-rays generated by the periodic patternof sub-sources of x-rays; a stage configured to hold an object to beimaged; and an x-ray detector comprising a two-dimensional array ofx-ray detecting elements, said object positioned between thebeam-splitting x-ray grating and the x-ray detector, said x-ray detectorpositioned to detect the x-rays diffracted by the beam-splitting x-raygrating and perturbed by the object to be imaged.
 2. The x-rayinterferometric imaging system of claim 1, in which a ratio (Z₂ ρ₂)/(Z₁ρ₁) for the second material and the first material is greater than 12,where Z₁ and ρ₁ are the atomic number and the mass density,respectively, of the first material and Z₂ and ρ₂ are the atomic numberand the mass density, respectively of the second material.
 3. The x-rayinterferometric imaging system of claim 1, in which the first materialis selected from the group consisting of: beryllium, diamond, graphite,silicon, boron nitride, silicon carbide, sapphire and diamond-likecarbon.
 4. The x-ray interferometric imaging system of claim 1, in whichthe plurality of discrete structures have similar shapes.
 5. The x-rayinterferometric imaging system of claim 1, in which the periodic patternof the plurality of discrete structures is a regular grid and a width inat least one dimension of one or more discrete structures of theplurality of discrete structures is less than 10 microns.
 6. The x-rayinterferometric imaging system of claim 1, in which the periodic patternof the plurality of discrete structures is a set of parallel lines and awidth in one dimension of one or more discrete structures of theplurality of discrete structures is less than 10 microns, and a lengthin a perpendicular dimension is greater than 20 microns.
 7. The x-rayinterferometric imaging system of claim 1, in which the phase shift ofthe beam-splitting x-ray grating is approximately π radians for thepredetermined x-ray wavelength.
 8. The x-ray interferometric imagingsystem of claim 1, in which the phase shift of the beam-splitting x-raygrating is approximately π/2 radians for the predetermined x-raywavelength.
 9. The x-ray interferometer imaging system of claim 1, inwhich the x-ray detector is positioned at a distance from thebeam-splitting x-ray grating that corresponds to an odd multiple of1/16^(th) of a Talbot Distance for the beam-splitting x-ray grating whenused with spherical wave x-rays of a predetermined wavelength spectrumand spatial coherence, the x-ray detector having a spatial resolution atleast three times a Talbot fringe period for a Talbot interferencepattern at said odd multiple of 1/16^(th) of the Talbot Distance for thebeam-splitting x-ray grating when used with x-rays of said predeterminedwavelength spectrum and spatial coherence.
 10. The x-ray interferometricimaging system of claim 1, in which an orientation of at least twodiscrete structures of the plurality of discrete structures of thetarget are such that, when simultaneously bombarded by electrons fromthe electron beam emitter, the x-rays generated by a first discretestructure of the at least two discrete structures overlap in part thex-rays generated by a second discrete structure of the at least twodiscrete structures, and the overlapping x-rays propagate togethertowards the beam-splitting x-ray grating.
 11. The x-ray interferometricimaging system of claim 1, wherein the stage is configured to adjust aposition of the object relative to the beam-splitting x-ray grating. 12.The x-ray interferometric imaging system of claim 11, wherein the stageis configured to move the object along each of three orthogonal axes andto rotate the object along each of three orthogonal axes.
 13. The x-rayinterferometric imaging system of claim 1, additionally comprising: ananalyzer grating placed in close proximity to a surface of the x-raydetector.
 14. The x-ray interferometric imaging system of claim 13, inwhich the analyzer grating comprises periodic structures that form anx-ray absorption grating, in which the periodic structures of theanalyzer grating have a period p₂ given approximately by:$p_{2} = {p_{0}\frac{D}{L}}$ where p₀ is the period of the periodicpattern of sub-sources of x-rays, D is the distance between thebeam-splitting x-ray grating and the analyzer grating, and L is thedistance between the target and the beam-splitting x-ray grating. 15.The x-ray interferometric imaging system of claim 13, wherein the stageis configured to adjust a position of the object relative to theanalyzer grating.
 16. The x-ray interferometric imaging system of claim1, additionally comprising: a cooling system comprising: a reservoir forstoring a cooling fluid; a channel within the substrate for conductingthe cooling fluid; an additional channel to conduct the cooling fluidfrom the reservoir to the channel within the substrate; an additionalchannel to conduct the cooling fluid from the channel within thesubstrate to the reservoir; and a pumping mechanism to pump the coolingfluid through the cooling system.
 17. An x-ray tomography systemcomprising: an x-ray source comprising: a vacuum chamber; an electronbeam emitter; and a target comprising: a substrate comprising a firstmaterial; and a plurality of discrete structures embedded in thesubstrate, the plurality of discrete structures comprising a secondmaterial that generates x-rays in response to electron irradiation, saidplurality of discrete structures arranged in a periodic pattern toproduce a periodic pattern of sub-sources of x-rays when irradiated byelectrons from the electron beam emitter; a beam-splitting x-ray gratingcomprising periodic structures that introduce a phase shift for apredetermined x-ray wavelength, the periodic structures comprisingtwo-dimensional structures arranged in a checkerboard pattern, saidbeam-splitting x-ray grating positioned to diffract x-rays generated bythe periodic pattern of sub-sources of x-rays; a stage configured tohold an object for tomographic data collection; and an x-ray detectorcomprising a two-dimensional array of x-ray detecting elements, saidobject positioned between the beam-splitting x-ray grating and the x-raydetector, said x-ray detector positioned to detect the x-rays diffractedby the beam-splitting x-ray grating and perturbed by the object to beimaged.
 18. The x-ray tomography system of claim 17, wherein the stageis configured to controllably change a position and an orientation ofthe object relative to the x-ray source.
 19. The x-ray tomography systemof claim 18, in which the stage is configured to controllably change anangle of incidence of the x-rays on the object.
 20. The x-ray tomographysystem of claim 19, in which the stage and the x-ray detector areconfigured to make a plurality of images of the object in which each ofthe plurality of, images is collected using a different setting for theangle of incidence of the x-rays on the object.
 21. An x-rayinterferometric imaging system comprising: a source of x-rayscomprising: a vacuum chamber; an electron beam emitter; and a targetcomprising: a substrate comprising a first material; and a plurality ofdiscrete structures embedded in the substrate, the plurality of discretestructures comprising a second material that generates x-rays inresponse to electron irradiation, said plurality of discrete structuresarranged in a periodic pattern to produce a periodic pattern ofsub-sources of x-rays when irradiated by electrons from the electronbeam emitter; a beam-splitting x-ray grating comprising periodicstructures that introduce a phase shift for a predetermined x-raywavelength, said beam-splitting x-ray grating positioned to diffractx-rays generated by the periodic pattern of sub-sources of x-rays; astage configured to hold an object to be imaged; and an x-ray detectorcomprising a two-dimensional array of x-ray detecting elements, saidobject positioned between the beam-splitting x-ray grating and the x-raydetector, said x-ray detector configured to detect the x-rays diffractedby the beam-splitting x-ray grating and perturbed by the object to beimaged, the x-ray detector positioned at a distance from thebeam-splitting x-ray grating that corresponds to an odd multiple of1/16^(th) of a Talbot Distance for the beam-splitting x-ray grating whenused with spherical wave x-rays of a predetermined wavelength spectrumand spatial coherence, the x-ray detector having a spatial resolution atleast three times a Talbot fringe period for a Talbot interferencepattern at said odd multiple of 1/16^(th) of the Talbot Distance for thebeam-splitting x-ray grating when used with x-rays of said predeterminedwavelength spectrum and spatial coherence.
 22. An x-ray interferometricimaging system comprising: a source of x-rays comprising: a vacuumchamber; an electron beam emitter; and a target comprising: a substratecomprising a first material; and a plurality of discrete structuresembedded in the substrate, the plurality of discrete structurescomprising a second material that generates x-rays in response toelectron irradiation, said plurality of discrete structures arranged ina periodic pattern to produce a periodic pattern of sub-sources ofx-rays when irradiated by electrons from the electron beam emitter; abeam-splitting x-ray grating comprising periodic structures thatintroduce a phase shift for a predetermined x-ray wavelength, saidbeam-splitting x-ray grating positioned to diffract x-rays generated bythe periodic pattern of sub-sources of x-rays; a stage configured tohold an object to be imaged, the stage configured to adjust a positionof the object relative to the beam-splitting x-ray grating bytranslating the object along each of three orthogonal axes and rotatingthe object along each of three orthogonal axes; and an x-ray detectorcomprising a two-dimensional array of x-ray detecting elements, saidobject positioned between the beam-splitting x-ray grating and the x-raydetector, said x-ray detector positioned to detect the x-rays diffractedby the beam-splitting x-ray grating and perturbed by the object to beimaged.